1. **State the problem:** Solve the equation $5(3x + 6)^2 + 9 = 44$ for $x$. 2. **Isolate the squared term:** Subtract 9 from both sides: $$5(3x + 6)^2 + 9 - 9 = 44 - 9$$ $$5(3x + 6)^2 = 35$$ 3. **Divide both sides by 5:** $$\cancel{5}(3x + 6)^2 = \cancel{5}7$$ $$ (3x + 6)^2 = 7$$ 4. **Take the square root of both sides:** Remember to consider both positive and negative roots. $$3x + 6 = \pm \sqrt{7}$$ 5. **Solve for $x$:** Subtract 6 from both sides: $$3x = -6 \pm \sqrt{7}$$ 6. **Divide both sides by 3:** $$\cancel{3}x = \frac{-6 \pm \sqrt{7}}{\cancel{3}}$$ $$x = \frac{-6 \pm \sqrt{7}}{3}$$ **Final answer:** $$x = \frac{-6 + \sqrt{7}}{3} \quad \text{or} \quad x = \frac{-6 - \sqrt{7}}{3}$$